International Journal of Scientific & Engineering Research, Volume 4, Issue 7, July-2013 1428
ISSN 2229-5518
IJSER © 2013
http://www.ijser.org
Optimal Unit Commitment Problem Solution
Using Real-Coded Particle Swarm Optimization
Technique
Ahmed Jasim Sultan
Abstract— This paper present real-coded particle swarm optimization RPSO is proposed to solve unit commitment
problem UCP. The unit commitment is the problem to determining the schedule of generating units subject to device and
operating constraints. The problem is decomposed in two sub-problem are unit commitment and economic dispatch that
are solved by RPSO. The UCP is formulated as the minimization of the performance index, which is the sum of
objectives (fuel cost, startup cost and shutdown cost) and some constraints (power balance, generation limits, spinning
reserve, minimum up time and minimum down time). The RPSO technique is tested and validated on 10 generation
units system for 24 hour scheduling horizon.
Index Terms— Real-Coded PSO, power system constraints, economic dispatch problem, optimal unit commitment.
—————————— ——————————
1. Introduction
nit commitment problem UCP is used to
economically schedule the generating units over a
short term planning horizon subjected to the forecasted
demand and other system operating constraints.
Generation scheduling involves the determination of
the startup and shutdown time points and the
generation levels for each unit over a given scheduling
period (usually 24 hour). Unit commitment plays an
important role in power system economic operation for
reasonable scheduling will save larger amount of fuel
cost and bring huge economic benefit [1, 2]. In solving
the UCP, generally two basic problems are involved,
namely the “unit commitment” decision and the
“economic dispatch” decision. The unit commitment
decision involves the determination of the generating
units to be running during each hour of the planning
horizon, considering the system capacity requirements,
including the spinning reserve, start up and shutdown
of unit constraints. The economic dispatch decision
involves the allocation of system demand and spinning
reserve capacity among the operating units during the
each specific hour of operation. The unit commitment is
considered as a non-linear, large-scaled, mixed integer
combinatorial optimization problem. The Previous UCP
method includes: priority list method, dynamic
programming, integer and linear programming,
Lagrangian relaxation, branch and bound, interior point
optimization, tabu search, simulated annealing,
artificial intelligence methods, evolutionary
programming etc. But each method exist some
difficulties such as: dimension disaster, searching
algorithm and convergence. This paper presents the
Real-Coded Particle Swarm Optimization technique for
the solution of the Unit Commitment Problem on 10
units during 24 hour.
2. UCP mathematical formulation
The main objective of the UCP is to minimization
cost turn-on and turn-off schedule of a set of electrical
power generating units to meet a load demand while
satisfying a set of operational constraints. Therefore the
objective function of the unit commitment problem is
expressed as the sum of fuel cost and startup cost for all
of the units over the whole scheduling periods [1, 2].
For N generating units and T hours the objective
function of the UCP can be written as follows:
F�P
i
t
,U
i,t
� = min(∑ ∑ �F
i
(P
i
t
) + ST
i,t
�1 − U
i,t−1
��U
i,t
N
i=1
T
t=1
)
…………… (1)
Where,
F(P
i
t
) is fuel cost of ith unit,
F
i
(P
i
t
)=a
i
P
i
2
+b
i
P
i
+c
i
ST
i,t
=
�
HST if T
i,down
< T
i,off
< T
i,cold
+T
i,down ,
CST if T
i,off
> T
i,cold
+ T
i,down
……..…. (2)
P
i
t
is amount of power produced by unit i at time t.
a
i
, b
i
and c
i
are cost parameters of ith unit.
U
i,t
is a control variable of unit i at time t.
HST
i
is hot startup cost of unit i (in dollars).
CST
i
is cold startup cost of unit i (in dollars).
T
i,cold
is cold start hour of unit i (in hours).
T
i,off
is continuously off time of unit i (in hours).
T
i,down
is minimum down time of unit i (in hours).
U
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